LangevinEvolution.java
package org.drip.sample.ckls;
import org.drip.dynamics.ito.R1WienerDriver;
import org.drip.dynamics.physical.LangevinEvolver;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>LangevinEvolver</i> implements the Noisy Elastic Relaxation Process in a Friction-Thermal Background.
* The References are:
*
* <br><br>
* <ul>
* <li>
* Doob, J. L. (1942): The Brownian Movement and Stochastic Equations <i>Annals of Mathematics</i>
* <b>43 (2)</b> 351-369
* </li>
* <li>
* Gardiner, C. W. (2009): <i>Stochastic Methods: A Handbook for the Natural and Social Sciences
* 4<sup>th</sup> Edition</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
* <b>World Scientific</b>
* </li>
* <li>
* Karatzas, I., and S. E. Shreve (1991): <i>Brownian Motion and Stochastic Calculus 2<sup>nd</sup>
* Edition</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Risken, H., and F. Till (1996): <i>The Fokker-Planck Equation – Methods of Solution and
* Applications</i> <b>Springer</b>
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/ckls/README.md">Analysis of CKLS Process Variants</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class LangevinEvolution
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv (
""
);
double timeWidth = 1.;
double temperature = 300.;
double restLength = 1.e-10;
double initialLength = 3.e-10;
double dampingCoefficient = 0.5;
double elasticityCoefficient = 1.0;
double[] timeArray =
{
0.0,
0.5,
1.0,
1.5,
2.0,
2.5,
3.0,
3.5,
4.0,
4.5,
5.0,
5.5,
6.0,
6.5,
7.0,
7.5,
8.0,
8.5,
9.0,
9.5
};
System.out.println (
"\t|-----------------------------------------------------------||"
);
System.out.println (
"\t| LANGEVIN SYSTEM EVOLUTION ||"
);
System.out.println (
"\t|-----------------------------------------------------------||"
);
System.out.println (
"\t| Temperature => " + temperature
);
System.out.println (
"\t| Rest Length => " + restLength
);
System.out.println (
"\t| Damping Coefficient => " + dampingCoefficient
);
System.out.println (
"\t| Elasticity Coefficient => " + elasticityCoefficient
);
System.out.println (
"\t|-----------------------------------------------------------||"
);
R1WienerDriver wienerDriver = new R1WienerDriver (
timeWidth
);
LangevinEvolver langevinEvolver = new LangevinEvolver (
elasticityCoefficient,
dampingCoefficient,
restLength,
temperature,
wienerDriver
);
System.out.println (
"\t| Correlation Time => " + langevinEvolver.correlationTime()
);
System.out.println (
"\t| Diffusion Coefficient => " + langevinEvolver.stokesEinsteinEffectiveDiffusionCoefficient()
);
System.out.println (
"\t| Equi-Partition Energy => " + langevinEvolver.equiPartitionEnergy()
);
System.out.println (
"\t| Volatility => " + langevinEvolver.cklsParameters().volatilityCoefficient()
);
System.out.println (
"\t| Mean-Reversion Level => " + langevinEvolver.cklsParameters().meanReversionLevel()
);
System.out.println (
"\t| Mean-Reversion Speed => " + langevinEvolver.cklsParameters().meanReversionSpeed()
);
System.out.println (
"\t|-----------------------------------------------------------||"
);
System.out.println();
System.out.println (
"\t|-----------------------------------------------------------||"
);
for (double time : timeArray)
{
System.out.println (
"\t| " + FormatUtil.FormatDouble (time, 1, 1, 1.) + " => " +
FormatUtil.FormatDouble (
langevinEvolver.fluctuationCorrelation (
time
), 1, 5, 1.
) + " | " + FormatUtil.FormatDouble (
langevinEvolver.fluctuationCovariance (
time
), 1, 25, 1.
) + " | " + FormatUtil.FormatDouble (
langevinEvolver.mean (
initialLength,
time
), 1, 15, 1.
)
);
}
System.out.println (
"\t|-----------------------------------------------------------||"
);
System.out.println();
double[][] aitSahaliaMLEAsymptote = langevinEvolver.aitSahaliaMLEAsymptote (
1.
);
System.out.println (
"\t|---------------------------------||"
);
System.out.println (
"\t| AIT SAHALIA MLE ASYMPTOTE ERROR ||"
);
System.out.println (
"\t|---------------------------------||"
);
org.drip.numerical.common.NumberUtil.Print2DArray (
"\t|\t",
aitSahaliaMLEAsymptote,
false
);
System.out.println (
"\t|---------------------------------||"
);
EnvManager.TerminateEnv();
}
}